Question

In △PQR , ∠P - ∠Q = 18° and ∠Q - ∠R = 12° . Find all the 3 angles of the triangle.​

Answer 1

<P-<Q=18. (1)

<Q-<R=12. (2)

From equation (1)

<P=18+<Q. (3)

We know that sum of all angles of triangle is 180

then <P+<Q+<R=180

putting the value of <P in this equation

18+<Q+<Q+<R=180

=2<Q+<R=180-18

then from equation (2) we get

<R=<Q-12 putting this value in that equation

=2<Q+<Q-12=162

=3<Q=162+12

=<Q=174/3

=<Q=58

then putting this value in equation (1)

<P-<Q=18

<P- 58=18

then <P= 58+18

<P=76

then putting this value in equation (2)

<Q-<R=12

58-<R=12

<R=46

then angles are 76, 58 ,46